Calculate the following expression: $$\frac{5^{2}-8}{5^{-15}}$$

Let's simplify the expression step by step. First, we calculate the numerator: $$5^2 - 8 = 25 - 8 = 17$$ Now, we have the expression: $$\frac{17}{5^{-15}}$$ To get rid of the negative exponent in the denominator, we can rewrite the expression using the property $$a^{-n} = \frac{1}{a^n}$$: $$5^{-15} = \frac{1}{5^{15}}$$ So, the expression becomes: $$\frac{17}{\frac{1}{5^{15}}}$$ Dividing by a fraction is the same as multiplying by its reciprocal: $$\frac{17}{\frac{1}{5^{15}}} = 17 \cdot 5^{15}$$ So, the final result is: $$17 \cdot 5^{15}$$ We can calculate $$5^{15}$$ which is equal to 30517578125. Thus: $$17 \cdot 30517578125 = 518798828125$$ So, the final result is 518798828125. Answer: 518798828125